Our resident expert on probability based attacks
is Dr Tristan Barnett, who discusses various
ways to win using mathematical techniques in his Probability
Based Attacks section of Smartgambler. The
page you are on gives an introductory overview of
probability theory.

Probability theory
is an important area of mathematics, with many applications
to real life. It is absolutely central to gambling.
It is not necessary to learn the math, provided you
can accept the simple facts presented in this segment.

Probability will not dance to your tune. In Zen,
the practitioner learns not to go against the flow.
Probability too is a great ally but a terrible foe.
Don't fight it. It is an area of ignorance for a surprisingly
large number of people and is rife with popularly
accepted myths and fallacies.

A smart gambler understands that blind chance does not play favourites, does not recognize 'lucky numbers', has no memory and no personality. It doesn't care whether you tap a card before looking at it or what amount you have placed on an outcome.

Everyone should know that if you toss ten heads
in a row it is still 50/50 whether it will be another
head, but many punters still allow irrational thoughts
that something must be 'due to happen' to affect their
gaming. The smart gambler, seeing ten heads in a row,
would back heads again just in case there is
a bias that is not apparent!

Confusion sometimes arises because of the different
likelihoods of a given event occurring before it starts,
compared to part of the way through the event.

Take the example above. Before you toss a coin you
can say with certainty that the probability of getting
ten heads in a row is exactly 1/2 * 1/2 * 1/2 * 1/2,
etc (keep multiplying ten times) which comes to one
chance in 1,024. But if we throw five heads in a row,
the probability of the next five tosses coming up
heads isn't one in 1,024 of course, it is one chance
in 32.

This is because the slate is cleaned, so
to speak, after each toss. Chance
has no memory. (Even if it did, how would we
know that somewhere else in the world it hadn't just
come up five tails in a row?)

Casinos generously pander to the ignorance of punters by providing little
pads and pencils to keep track of utterly meaningless sequences of Roulette
numbers that have occurred. The money spent on ridiculous items such as this
could be better given back to punters by providing slightly better odds or cheaper
bar prices.

Random number sequences

Are the chances of 1,2,3,4,5,6 coming up in a Lotto
draw any less than a so called 'random' sequence?
Of course not! The chances of getting 1,2,3,4,5,6
out of a possible 40 balls is very small indeed, but
it's exactly the same probability as any other six
numbers.

The fact that some humans consider numbers one through
six, or a birth date, or whatever, as some special
numerical sequence, is completely lost on the balls
themselves as they roll out of their cage. Any combination
of numbers in a random selection such as Lotto is
equally as likely to occur as any other. Given that
chance has no memory it is also clear that an analysis
of the frequency with which past numbers have fallen,
cannot help to predict future numbers.

Lotto is a bad game to play purely in terms of percentage
returns, you are paying for a pleasant dream really,
but there are ways of maximising any prospective returns
based on the point raised above. (See Lotto
section)